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A 5-Minute Tour of Beamer’s SimplestFeatures
Norm MatloffDept. of Computer Science
University of California, Davis
July 17, 2005
Outline
A Question from Grade School
(Illustrating BEAMER’s \pause command.)
A couple of years ago, a fifth-grade teacher asked me toexplain to her the reasoning behind the “invert and multiply”rule for dividing fractions, e.g.
45÷ 2
3=
45× 3
2Let’s try to find answers understandable by fifth graders (atleast the more patient ones).
A Question from Grade School
(Illustrating BEAMER’s \pause command.)
A couple of years ago, a fifth-grade teacher asked me toexplain to her the reasoning behind the “invert and multiply”rule for dividing fractions, e.g.
45÷ 2
3=
45× 3
2
Let’s try to find answers understandable by fifth graders (atleast the more patient ones).
A Question from Grade School
(Illustrating BEAMER’s \pause command.)
A couple of years ago, a fifth-grade teacher asked me toexplain to her the reasoning behind the “invert and multiply”rule for dividing fractions, e.g.
45÷ 2
3=
45× 3
2Let’s try to find answers understandable by fifth graders (atleast the more patient ones).
Cookie Approach
Here let’s just use intuition, understandable by fifth graders.
If we give 1/3 of a cookie to each person, how many people canwe feed with 1 cookie?Obviously, the answer is 3.So we’ve derived the “invert and multiply” rule in a special case:
1÷ 13
= 3
Cookie Approach
Here let’s just use intuition, understandable by fifth graders.If we give 1/3 of a cookie to each person, how many people canwe feed with 1 cookie?
Obviously, the answer is 3.So we’ve derived the “invert and multiply” rule in a special case:
1÷ 13
= 3
Cookie Approach
Here let’s just use intuition, understandable by fifth graders.If we give 1/3 of a cookie to each person, how many people canwe feed with 1 cookie?Obviously, the answer is 3.So we’ve derived the “invert and multiply” rule in a special case:
1÷ 13
= 3
Cookie Approach
But what if we give 2/3 of a cookie, not 1/3, to each person?We’re giving 2× as much per person.So we can feed only 1/2 as many people.So we feed 1
2 × 3 = 32 .1
So we’ve derived the “invert and multiply” rule in another case:
1÷ 23
=32
1One person gets only a half share.
Cookie Approach
Now, suppose we have only 4/5 of a cookie.Then we can feed only 4/5 as many people, i.e.
45× 3
2people
So we’ve derived the “invert and multiply” rule in the generalcase:
45÷ 2
3=
45× 3
2
Cookie Approach
Now, suppose we have only 4/5 of a cookie.Then we can feed only 4/5 as many people, i.e.
45× 3
2people
So we’ve derived the “invert and multiply” rule in the generalcase:
45÷ 2
3=
45× 3
2
Outline
A Geometry Proof
(Illustrating BEAMER’s \uncover command.)
TheoremThe angles in a triangle sum to 180◦.
Plan: Extend AC past C to D. Draw CE parallel to AB.
A Geometry Proof
(Illustrating BEAMER’s \uncover command.)
TheoremThe angles in a triangle sum to 180◦.Plan: Extend AC past C to D. Draw CE parallel to AB.
Proof.1. u = y
Alternate angles of a transveral.2. v = x Consecutive interior angles of a transveral3. z+u+v = 180◦ ACD is a straight line.4. z+y+x = 180◦ Substitution from Steps 1 and 2.
Proof.1. u = y Alternate angles of a transveral.
2. v = x Consecutive interior angles of a transveral3. z+u+v = 180◦ ACD is a straight line.4. z+y+x = 180◦ Substitution from Steps 1 and 2.
Proof.1. u = y Alternate angles of a transveral.2. v = x
Consecutive interior angles of a transveral3. z+u+v = 180◦ ACD is a straight line.4. z+y+x = 180◦ Substitution from Steps 1 and 2.
Proof.1. u = y Alternate angles of a transveral.2. v = x Consecutive interior angles of a transveral
3. z+u+v = 180◦ ACD is a straight line.4. z+y+x = 180◦ Substitution from Steps 1 and 2.
Proof.1. u = y Alternate angles of a transveral.2. v = x Consecutive interior angles of a transveral3. z+u+v = 180◦
ACD is a straight line.4. z+y+x = 180◦ Substitution from Steps 1 and 2.
Proof.1. u = y Alternate angles of a transveral.2. v = x Consecutive interior angles of a transveral3. z+u+v = 180◦ ACD is a straight line.
4. z+y+x = 180◦ Substitution from Steps 1 and 2.
Proof.1. u = y Alternate angles of a transveral.2. v = x Consecutive interior angles of a transveral3. z+u+v = 180◦ ACD is a straight line.4. z+y+x = 180◦
Substitution from Steps 1 and 2.
Proof.1. u = y Alternate angles of a transveral.2. v = x Consecutive interior angles of a transveral3. z+u+v = 180◦ ACD is a straight line.4. z+y+x = 180◦ Substitution from Steps 1 and 2.
Outline
More Advanced Features of BEAMER
I This tour just scratches the surface.
I BEAMER has enough features to fill a 210-page usermanual!
I Advanced example: http://latex-beamer.sourceforge.net/beamerexample1.pdf.
More Advanced Features of BEAMER
I This tour just scratches the surface.I BEAMER has enough features to fill a 210-page user
manual!
I Advanced example: http://latex-beamer.sourceforge.net/beamerexample1.pdf.
More Advanced Features of BEAMER
I This tour just scratches the surface.I BEAMER has enough features to fill a 210-page user
manual!I Advanced example: http://latex-beamer.sourceforge.net/beamerexample1.pdf.